The domain structure model can account for
the color confinement in terms of the interaction of the Wilson loops with the center domains [1]}, [2]}. In the model, it is assumed that the QCD vacuum is filled with the domains of the center-vortex type corresponding to the non-trivial center element and of the vacuum type corresponding to the identity element. In some literatures given as a particular proposal for SU(3) [3]} and SU(4) [4]}, [5]}, the core of domains is corresponding to only one Cartan generator which lead to some shortcomings.
